As I see it, the guy is putting himself into a loop where he is copying his mind every 15 minutes then reloading into himself. The only way out is an interruption by somebody else, and no one every visits the unnamed character.

So given that, it is not obvious that that the story is going in this direction I would leave the plot as it stands. That way the reader is left wondering how the unnamed character going to get out of the mess

The concept is really good. First, understanding of course this is my opinion, he spends a lot of time thinking about what he has done, and very little time actually doing anything. If you want to aviod the dreaded info dump, you could add some form of acting, and use the decription to explain why he's doing what he's doing.

I like the ending, but think it could be made stronger. I'm not sure how to make it stronger, perhaps -I grasp at straws- make the first few moments more traumatic, or more of a "eureka" moment. Or both. Make the scene stand out so when it comes around again the reader doesn't have to go back and make sure it matches.

And, point of order :

Whenever he used the BST (Brain Sequential Transponder, as he named it) he had to turn off everything else, since the amount of energy needed was very close the maximum capacity of his laboratory.

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If you are talking about electrical capacity, we would usually say "maximum amperage". If he is self sufficient, you might say "maximum capacity of his generator". One would have to add a higher capacity breaker in order to use the entire load. --all this is way more information than the story needs, but sounding right is better.

So the first time he ran it, the machine was set to download, and 24 hrs later he switched to upload. Then he woke up restored, and 24 hrs later (and 48 hrs, 72 hrs, ...) he noticed it was already switched to upload. Maybe he has a simple but efficient helper robot that helped him get up from the couch and doesn't get in the way, or he noticed his reflection at the last moment. Any story can be improved by making it about 10% shorter (not recursively).